PSY 307 One-Way Between Subjects ANOVA

t-tests

used when you want to compare two groups on some criteria

its inefficient, time consuming, and every time you run a t-test you run the risk of committing a type I error

Why can't we use multiple t-tests to compare more than 2 groups?

0.95 ^x

x = the number of t-tests you would need to run

How to calculate the chances of NOT making a type I error

1 - (chances of NOT making a type I error) = the probability of a type I error

How to calculate the chances of making a type I error

at least three

How many levels are required for an ANOVA

One-way ANOVA

There is one independent variable with more than two groups

Two-way ANOVA

There are two independent variables each with more than two groups

Repeated Measures ANOVA

The same participants take part in each of the 3+ levels of the IV

Mixed ANOVA

There are one or more between-subject variables and one or more within subject variables

MANOVA

There is more than one dependent variables

Between-subjects ANOVA

compares means of three or more different groups of people, measured at the same time

only one IV (with at least three levels)

What does one-way refer to?

participants are randomly assigned to one group

What does between subjects refer to?

*same as the t-test

1. homogeneity of variance

2. groups are independent

3. normally distributed and continuous DV

Assumption of the One-Way Between Subjects ANOVA

Not always, control groups may or may not be necessary depending on the research question(s)

Is there always a control group in a One-Way Between Subjects ANOVA?

When

- H0: all groups are equal to each other

- Reject H0 when at least two of the groups are different

When do you perform post hoc tests (f ratio testing)

post hoc tests

tells us where differences are to further understand broad f ratios

As many as there are the levels of the IV

How many alternative hypotheses are there in a one-way between subjects ANOVA?

Analysis of variance

What does ANOVA stand for

F statistic

compares the amount of variability between groups against the amount of variability within each group

between group variance (SSB)

the distance or deviation of raw scores from the grand mean

within group variance (SSW)

- similar to pooled variances

the distance or deviation of raw scores means from the group mean

Ronald Fischer who set the alpha value

Who is the F statistics named after?

SS/df

mathematical representation for variance where squareness highlights the difference among our groups

No, the F stat is only 1 tailed

Is the F stat. two tailed?

At least greater than 1

- cannot be negative or zero as this means there is no difference among the groups at all, this is very unlikely

To be considered to being significant, what should the F stat. be?

SST = SSB + SSW

mathematical representation for total variance

Grand mean

mean for all our data points

We want the SSB to be bigger than the SSW

what value to we want to be large and which smaller?

SSB

represents IV

SSW

represents random error

k

number of groups or levels of the IV

n1, n2, n3...

number of people in each group

N

the total number of people

EXij

the sum of scores for each group

EXi

the total sum of scores from all groups

EXi^2

the total squared sum of scores (all groups)

k-1

number of groups - 1

N-k

total number of participants - groups

N-1

total number of participants - 1

dfn/dfd from our source table

What do we use to find the Fcrit. on the F table

high;low

When looking at our source table, we want between group variance to be _ and within group variance to be _ to produce significant results

effect size and statistical power

decreasing within group variances increases...

To ensure that changes in IV are responsible for changes in the DV

Why do we want small within group variance?

more

less variance and overlap between samples = _ significant results

less

more variance and more overlap between samples = _ significant results

.01 = small effect size

.06 = medium effect size

.14 = large effect size

What are the values for partial eta squared and what do they mean?

Partial eta squared

tells us how much variability (variance)can be accounted for by an independent variables

Because Cohen's D only works for 2 groups

Why can't we use Cohen's D for effect size in the one-way ANOVA

When we have significant results

When do we run Post Hoc tests?

1) All three groups are different

2) One condition differs from the other two

3) Two conditions differ from the other one

Three possible ways groups could be different from one another as determined by Post Hoc Tests?

Yes!

Are all groups included in the alternative hypothesis?

Tukey's Honestly Significant Difference (HSD)

can investigate multiple comparison of means (when the F is significant). If it is, we use its' formula

q in HSD

level of significance for the total number of groups being compared

decreased (easier to detect differences); increased (harder to detect differences)

For HSD: increased n = _ standard error and decreased n = _ standard error

Type I error

Tukey's HSD helps us find more conservative findings which combat against...

1) Arrange the means from small to largest

2) Subtract the means from each other (largest-smallest)

3) Compare the HSD value to the mean difference for the groups

What are the three rules of Post Hoc difference table?

significant results (compare each mean group with HSD)

If mean difference for the group is greater than HSD, we have what results?

SSerror (random error)

SSw=